Implications of second-order wave generation for physical modelling of force and run-up on a vertical wall using wave groups

Experiments are contaminated by second-order error waves at sub- and super-harmonic frequencies when first-order wave generation is used. Herein, we investigate by experiment the implications of second-order wave generation theory for dynamic wave force and run-up on a vertical wall in shallow to intermediate water depth (𝑘0⁢𝑑=0.5−1.1). Results of short-duration experiments using focused wave groups generated according to first- and second-order theory are compared. We isolate linear, sub-, and super-harmonic contributions using combinations of inverted wave group time series and filtering. We derive theoretical predictions for narrow-banded second-order wave groups interacting with a vertical wall and use this to calculate depth-integrated force and run-up on the wall, which show close agreement with measured data. Comparisons reveal that sub-harmonic error waves are increasingly important in shallow depth, increasing wave run-up by up to 67% and dynamic force by up to 75% at 𝑘0⁢𝑑=0.6 when compared to the case of correct (second-order) generation in a relatively short flume.